Solitons, Nonlinear Evolution Equations and Inverse Scattering

1991 ◽  
Author(s):  
M. A. Ablowitz ◽  
P. A. Clarkson
Keyword(s):  
Inverse Scattering ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations

scholarly journals On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension

2004 ◽  
Vol 2004 (58) ◽  
pp. 3117-3128
Author(s):  
H. H. Chen ◽  
J. E. Lin
Keyword(s):  
Inverse Scattering ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Spatial Dimension ◽  
Nonlinear Evolution Equations ◽  
Scattering Problems ◽  
Direct Construction ◽  
Inverse Scattering Problems ◽  
Petviashvili Equation ◽  
The One

We present a method to construct inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension. The temporal component is the adjoint of the linearized equation and the spatial component is a partial differential equation with respect to the spatial variables. Although this idea has been known for the one-spatial dimension for some time, it is the first time that this method is presented for the case of the higher-spatial dimension. We present this method in detail for the Veselov-Novikov equation and the Kadomtsev-Petviashvili equation.

On Nonlinear Equations Amenable to the Inverse Scattering Method

1975 ◽  
Vol 53 (1) ◽  
pp. 58-61 ◽  
Author(s):  
J. G. Kingston ◽  
C. Rogers
Keyword(s):  
Inverse Scattering ◽  
Initial Value Problem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Inverse Scattering Method ◽  
Nonlinear Evolution Equations ◽  
Scattering Method ◽  
Initial Value ◽  
Physical Importance ◽  
Extensive Class

The inverse scattering method can be used to solve the initial value problem for various nonlinear evolution equations of physical importance. Here an extensive class of equations for which the technique is available is delimited.

Sign in / Sign up

Export Citation Format

Share Document